MATH Documents

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Lecture 6
Basic laws of distribution of discrete random variables (continuing)
4. Hypergeometric distribution
Hypergeometric distribution is widely used in practice of statistical acceptance control by quality of industrial
production, in the problems con

Lecture 7
Numerical characteristics of variation series
Variation series allow receiving a first representation on a studied distribution. Further it is necessary to
investigate numerical characteristics of distribution.
Arithmetic mean of a variation ser

Lecture 12
Testing statistical hypotheses
A hypothesis on a kind of unknown distribution or on parameters of known distributions is said
to be statistical. A tested hypothesis H0 is called null (basic). The hypothesis H1 that contradicts
the null hypothes

LECTURE 8
Statistical estimations of parameters of distribution
Mathematical theory of sampling is based on properly random sample. Arithmetic means of
distribution of an attribute in a parent and sample populations are parent and sample means
respectivel

LECTURE 9
Method of moments
According to the method of moments offered by K. Pearson for finding pointwise estimators of
unknown parameters of a given distribution is to equate a certain amount of the sampling
moments (initial M k either central mk , or t

Lecture 11
Interval estimators of parameters
Pointwise estimators of an unknown parameter are good as initial results of processing
observations. Their disadvantage is that it is unknown with which precision they give an
estimated value. For samples of sm

Lecture 10
Method of maximal (the greatest) plausibility
The basic method of obtaining estimations of parameters of parent population on sample data is
the method of maximal plausibility offered by R. Fisher.
The method of maximal plausibility of pointwis